When actions speak louder than words then why is a pen mightier than a sword?

We have all been hearing the cliche expression, “actions speak louder than words” and are apparently in doldrums when we hear such banal quotes. While I was making running notes in a lecture, this absurd statement crossed my mind, “a pen is mightier than a sword.” A sword is analogous to action and a pen to words. This judgement draws me to a state of confusion and conclusion that words exert more power than actions which blatantly contradicts the former quote.
These contrary expressions are gnawing my brain ever since I thought of them.